Answer :
To solve the problem using the given system of equations, we need to find an equation that represents the relationship between the two given equations:
1. The first equation is: [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. The second equation is: [tex]\( y = 7x^4 + 2x \)[/tex]
To find a common equation, we can set the two expressions for [tex]\( y \)[/tex] equal to each other because they both represent the same [tex]\( y \)[/tex] value:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Next, we rearrange the equation to have all terms on one side, resulting in a single equation set to zero:
1. Subtract [tex]\( 7x^4 + 2x \)[/tex] from both sides:
[tex]\[ 0 = 7x^4 + 2x - 3x^3 + 7x^2 - 5 \][/tex]
This simplifies to:
[tex]\[ 7x^4 - 3x^3 + 7x^2 + 2x - 5 = 0 \][/tex]
This polynomial equation [tex]\( 7x^4 - 3x^3 + 7x^2 + 2x - 5 = 0 \)[/tex] is the equation that can be solved using the given system of equations.
In summary, by equating the two original equations and rearranging terms, we derive the polynomial equation that represents their relationship.
1. The first equation is: [tex]\( y = 3x^3 - 7x^2 + 5 \)[/tex]
2. The second equation is: [tex]\( y = 7x^4 + 2x \)[/tex]
To find a common equation, we can set the two expressions for [tex]\( y \)[/tex] equal to each other because they both represent the same [tex]\( y \)[/tex] value:
[tex]\[ 3x^3 - 7x^2 + 5 = 7x^4 + 2x \][/tex]
Next, we rearrange the equation to have all terms on one side, resulting in a single equation set to zero:
1. Subtract [tex]\( 7x^4 + 2x \)[/tex] from both sides:
[tex]\[ 0 = 7x^4 + 2x - 3x^3 + 7x^2 - 5 \][/tex]
This simplifies to:
[tex]\[ 7x^4 - 3x^3 + 7x^2 + 2x - 5 = 0 \][/tex]
This polynomial equation [tex]\( 7x^4 - 3x^3 + 7x^2 + 2x - 5 = 0 \)[/tex] is the equation that can be solved using the given system of equations.
In summary, by equating the two original equations and rearranging terms, we derive the polynomial equation that represents their relationship.
